Learn Extracted exam questions AP Physics 2 2022 Free Response
2022 Free Response
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Students are investigating electromagnetic wave phenomena in transparent media. They use a string to support a stationary thin, rectangular block of mass $m_b$, volume $V_b$, and density $\rho_b$. The block has two narrow slits in its center and is submerged in a glass tank containing water with density $\rho_w$, as shown above.
[Diagram: A rectangular glass tank of water, viewed from the side. A string hangs from the top of the tank down to a thin rectangular block suspended in the water; the block has two narrow slits in its center. A laser is aimed horizontally at the block from outside the left wall of the tank. A screen is shown near the bottom right, inside the tank.]
On the dot below, which represents the block, draw and label the forces that are exerted on the block. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot.
[A single dot is shown, representing the block, for the student to draw force vectors on.]
Derive an expression for the force exerted on the block by the string in terms of the given quantities and physical constants, as appropriate.
A monochromatic laser beam is incident perpendicular to the wall of the tank. The beam passes through the slits in the block. An interference pattern is formed on the screen inside the tank. The water is then replaced with a clear fluid with a greater index of refraction than that of water. In a coherent, paragraph-length response, describe how the greater index of refraction of the new fluid affects the interference pattern. Explain your reasoning in terms of speed, frequency, and wavelength of the light.
[Diagram: The same tank, now containing a fluid instead of water, with a triangular prism placed in it in place of the block. A laser enters from the left, perpendicular to the tank wall, and its path is shown as a dotted line traveling through the fluid to the prism; after passing through the prism the beam is refracted and travels (dotted line) to a screen on the right, striking it at a labeled point $P$.]
The block is replaced by a triangular prism, as shown above. The path of the beam is indicated by the dotted line, and the beam reaches the screen at point $P$. The fluid is then removed from the tank, and the prism is surrounded by air. Predict whether the beam will reach the side of the tank above point $P$, at point $P$, or below point $P$ when the prism is surrounded by air. Support your answer using physics principles.
[Diagram: Two circuits, each drawn with a battery symbol on the left. The first circuit has a battery connected to two resistors in parallel branches, labeled $A$ and $B$ (both drawn as resistor zig-zag symbols). The second circuit has a battery connected to two resistors in series, labeled $C$ (top) and $D$ (bottom, both zig-zag resistor symbols).]
Students perform an experiment with a battery and four resistors, A, B, C, and D. The resistance of resistors A and C is $R_A = R_C = R$. The resistance of resistors B and D is $R_B = R_D = 2R$. The students create the two circuits shown above and measure the potential differences $\Delta V_A$, $\Delta V_B$, $\Delta V_C$, and $\Delta V_D$ across resistors A, B, C, and D, respectively.
From greatest to least, rank the magnitudes of the potential differences across the resistors. Use "1" for the greatest magnitude, "2" for the next greatest magnitude, and so on. If any potential differences have the same magnitude, use the same number for their ranking.
____$\Delta V_A$ ____$\Delta V_B$ ____$\Delta V_C$ ____$\Delta V_D$
Justify your answer.
In another experiment, the students have a capacitor with unknown capacitance $C_U$. They want to determine $C_U$ by using a battery of potential difference 4.5 V and several other capacitors of known capacitance. They create circuits with the battery, the unknown capacitor, and one of the capacitors of known capacitance. The students wait until the capacitors are fully charged and then record the potential difference $\Delta V_{known}$ across the known capacitor and the potential difference $\Delta V_U$ across the unknown capacitor. Their data are shown in the table on the following page.
| Known Capacitance of Capacitors (μF) | $\Delta V_{known}$ (V) | $\Delta V_U$ (V) |
|---|---|---|
| 200 | 0.91 | 3.53 |
| 300 | 0.65 | 3.74 |
| 400 | 0.51 | 3.95 |
| 500 | 0.42 | 4.06 |
| 600 | 0.36 | 4.17 |
Calculate the amount of charge on the capacitor of known capacitance of 200 μF in the students' experiment.
Briefly explain why the data in the table provide evidence that the capacitors are connected in series.
Briefly explain why connecting the capacitors in parallel would not provide enough information to determine the capacitance of the unknown capacitor if the only measuring device available is a voltmeter.
The students want to produce a linear graph of the data so that the capacitance $C_U$ of the unknown capacitor can be determined from the slope of the best-fit line for the data.
Indicate two quantities that could be plotted to produce the desired graph. Use the empty columns of the data table in part (b) to record any values that you need to calculate.
Vertical axis ________________ Horizontal axis ________________
Label the axes below and provide an appropriate scale with units. Plot the data points for the quantities indicated in part (c)(i) on the axes and draw a best-fit line.
[A blank grid of dashed gridlines, unlabeled axes, provided for the student to label, scale, and plot the best-fit line on.]
Using your best-fit line, determine the capacitance of capacitor $C_U$.
[Diagram: A circle representing the electron's circular orbit of radius $r$ around a stationary proton at the center. The electron, labeled with a minus sign, is on the circle at upper left, with an arrow pointing along the circle indicating its direction of motion; a line labeled $r$ connects the electron to the central proton, labeled with a plus sign. Note: Figure not drawn to scale.]
A hydrogen atom can be modeled as an electron in a circular orbit of radius $r$ about a stationary proton, as shown above. The gravitational force between the proton and electron is negligible compared to the electrostatic force between them.
Derive an equation for the speed $v$ of the electron in terms of $r$ and physical constants, as appropriate.
Derive an equation for the total energy of the atom in terms of $r$ and physical constants, as appropriate.
When the hydrogen atom absorbs a photon, the electron moves to an orbit with a larger radius and the total energy of the atom increases. Is your equation for the energy derived in part (b) consistent with this description of the model of a hydrogen atom absorbing a photon? Explain why the equation is or is not consistent.
Experiments show that a hydrogen atom can absorb a photon of frequency $3.2 \times 10^{15}$ Hz.
Calculate the energy of a photon with this frequency.
A student claims that when a hydrogen atom absorbs a photon at this frequency, the energy could be converted into mass, adding an electron to the atom. Calculate the amount of energy needed to create a particle with the mass of an electron and determine whether or not there is sufficient energy gained by the atom to add another electron.
[Diagram: Two bar charts side by side, titled "Before Photon Absorbed" and "After Photon Absorbed." Each chart has a vertical axis with two bars labeled $U_E$ and $K$. In the left ("Before") chart, a dashed horizontal line marks a positive level $K_i$ and a dashed horizontal line below zero marks a negative level $U_{E,i}$; the $U_E$ bar extends from 0 down to $U_{E,i}$ (negative), and the $K$ bar extends from 0 up to $K_i$ (positive). The right ("After") chart shows only the zero line, with both bars blank for the student to draw.]
The left bar chart in the figure above is complete and represents the initial electric potential energy $U_{E,i}$ of the atom and the initial kinetic energy $K_i$ of the electron before the photon is absorbed. In the space provided on the right, draw a bar chart to represent a possible final electric potential energy of the atom and final kinetic energy of the electron.
[Diagram: A long straight horizontal wire carrying current $I$ directed to the left (shown with a dashed line and an arrow labeled $I$ pointing left). Above the wire, at a distance $d$, is a dot representing a charged object. Two force vectors are drawn from the dot: $F_M$ pointing straight up, and $F_E$ pointing straight down (toward the wire). A velocity vector $v$ points to the left from the charged object.]
At the instant shown above, a negatively charged object is moving to the left with constant velocity $v$ near a long, straight wire that has a current $I$ directed to the left. The region contains a uniform electric field of magnitude $E$, and the charged object is at a distance $d$ from the wire. The figure shows the electric and magnetic forces, $F_E$ and $F_M$, respectively, exerted on the charged object.
Derive an expression for $v$ in terms of $E$, $d$, $I$, and physical constants, as appropriate.
[Diagram: The charged object has been removed. A square coil labeled "Coil" with side length $2L$ is shown above the same long straight wire carrying current $I$ (dashed line, arrow pointing left). The bottom side of the coil is a distance $L$ above the wire; a point $P_1$ is marked on the bottom side of the coil, and a point $P_2$ is marked on the top side of the coil. Vertical distance markers show $L$ from the wire to the bottom of the coil, and $L$ for each half of the coil's height (labeled $L$, $L$, $L$ from the wire up to $P_2$), with a horizontal dashed midline shown across the coil.]
The charged object is removed, and a square coil with side length $2L$ is placed near the long, straight wire, as shown above. The bottom of the coil is a distance $L$ from the wire. The magnitude of the magnetic field due to the current in the wire is $3B_0$ at point $P_1$ and $B_0$ at point $P_2$.
Write an "X" at a location on the figure where the magnitude of the magnetic field is $2B_0$. Briefly justify your reasoning.
Over a time interval of 2.0 s, the current in the wire is decreased. The initial magnetic flux through the coil is $5.0 \times 10^{-5}\ \text{T}\cdot\text{m}^2$ and the final magnetic flux through the coil is $1.0 \times 10^{-5}\ \text{T}\cdot\text{m}^2$. The coil has a total resistance of 10 Ω. Calculate the magnitude of the average current in the coil during the 2.0 s time interval.
[Diagram: A power supply connects via wires to a round coil of wire. A square coil is positioned directly above and concentric with the round coil, oriented horizontally with a dashed vertical axis line through the center of both coils. A part of the square coil is cut/removed, and the two ends from that gap are connected by wires to a lightbulb, which is shown lit.]
The wire is removed and the square coil is positioned so that the coil is directly above and concentric with a round coil of wire connected to a power supply. A part of the square coil is removed and a lightbulb is connected to the coil, as shown above.
During a short time interval, the current in the power supply is constantly increasing. Use physics principles to explain why the lightbulb is lit during the entire time interval.